Tetrahedron equation and quantum R matrices for q-oscillator representations

30th International Colloquium on Group Theoretical Methods in Physics

Kuniba, A.^1 ; Okado, M.^2

Graduate School of Arts and Sciences, University of Tokyo, Komaba

153-8902, Japan^1

Department of Mathematics, Osaka City University, Osaka

558-8585, Japan^2

关键词: R matrices;    Tensor products;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012051/pdf
DOI  :  10.1088/1742-6596/597/1/012051

来源: IOP

【 摘 要 】

We review and supplement the recent result by the authors on the reduction of the three dimensional R (3d R) satisfying the tetrahedron equation to the quantum R matrices for the q-oscillator representations of Uq(D(2)), Uq(A(2)2n) and Uq(C(1)n). A new formula for the 3d R and a quantum R matrix for n = 1 are presented and a proof of the irreducibility of the tensor product of the q-oscillator representations is detailed.